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In this paper, we study the existence and uniqueness of solutions to a class of non-Lipschitz G-BSDEs and the corresponding stochastic recursive optimal control problem. More precisely, we suppose that the generator of G-BSDE is uniformly…
This paper is concerned with a Stackelberg game of backward stochastic differential equations (BSDEs), where the coefficients of the backward system and the cost functionals are deterministic, and the control domain is convex. Necessary and…
In this paper, we study a multi-dimensional backward stochastic differential equation (BSDE) with oblique reflection, which is a BSDE reflected on the boundary of a special unbounded convex domain along an oblique direction, and which…
An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional. The coefficients and the weighting matrices in the cost functional are all assumed to be deterministic.…
A Deterministic affine quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the value function is…
Mean field optimal control problems are a class of optimization problems that arise from optimal control when applied to the many body setting. In the noisy case one has a set of controllable stochastic processes and a cost function that is…
This paper investigates the optimal control problem for a class of parabolic equations where the diffusion coefficient is influenced by a control function acting nonlocally. Specifically, we consider the optimization of a cost functional…
This article is the starting point of a series of works whose aim is the study of deterministic control problems where the dynamic and the running cost can be completely different in two (or more) complementary domains of the space $\R^N$.…
This paper investigates the convergence properties of the upwind difference scheme for the Hamilton--Jacobi--Bellman (HJB) equation, a central partial differential equation in optimal control theory. First, assuming the existence of a…
We introduce and study a new class of optimal switching problems, namely switching problem with controlled randomisation, where some extra-randomness impacts the choice of switching modes and associated costs. We show that the optimal value…
In this paper, we study reflected backward stochastic differential equation (reflected BSDE in abbreviation) with rank-based data in a Markovian framework; that is, the solution to the reflected BSDE is above a prescribed boundary process…
Controlling the stochastic dynamics of biological populations is a challenge that arises across various biological contexts. However, these dynamics are inherently nonlinear and involve a discrete state space, i.e., the number of molecules,…
We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
The dynamic programming approach for the control of a 3D flow governed by the stochastic Navier-Stokes equations for incompressible fluid in a bounded domain is studied. By a compactness argument, existence of solutions for the associated…
We explore the approximation of feedback control of integro-differential equations containing a fractional Laplacian term. To obtain feedback control for the state variable of this nonlocal equation we use the Hamilton--Jacobi--Bellman…
We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…
We are interested in stochastic control problems coming from mathematical finance and, in particular, related to model uncertainty, where the uncertainty affects both volatility and intensity. This kind of stochastic control problems is…
We obtain the variational equations for backward stochastic differential equations in recursive stochastic optimal control problems, and then get the maximum principle which is novel. The control domain need not be convex, and the generator…
This paper studies {a} mixed singular/switching stochastic control problem for a multidimensional diffusion with multiples regimes on a bounded domain. Using probabilistic, partial differential equation (PDE) and penalization techniques, we…